New ansatze that involve hyperbolic functions are introduced to handle modified fifth-order KdV equations. A set of entirely new compactons, solitary patterns and periodic solutions is constructed. The study introduces new approaches and presents useful guidance for other related problems.

In this work, we study compact and noncompact dispersive structures formed by a class of nonlinear dispersive equations. We show that the focusing branches provide compactons solutions: solitons with compact support. We also show that the defocusing branches generate solitary patterns solutions....

In this work, we present an analytic study of the compactons structures in a class of nonlinear dispersive equations. The compactons: new form of solitary waves with compact support and width independent of amplitude, are formally constructed. We further establish solitary patterns solutions for...

Travelling wave solutions for the Boussinesq-double sine-Gordon (B-sine-Gordon) equation, the Boussinesq-double sinh-Gordon equation (B-sinh-Gordon), and the Boussinesq-Liouville (BL) equation are formally derived. The approach rests mainly on the variable separated ODE method. Distinct sets of...

In this work, a generalized time-dependent variable coefficients combined KdV–mKdV (Gardner) equation arising in plasma physics and ocean dynamics is studied. By means of three amplitude ansatz that possess modified forms to those proposed by Wazwaz in 2007, we have obtained the bell type...